Mark Bakker^a and Erik I. Anderson^a
a Department of Biological and Agricultural Engineering, University of Georgia, Athens, GA 30602, USA
^b Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA

Received 3 April 2001;  accepted 23 October 2001.  Available online 29 November 2001.

Author Keywords: Groundwater; Hodograph; Analytic; Lake

1. Introduction

In mathematical models, groundwater flow fields are characterized by the singularities present in and on the boundary of the flow domain. It is difficult to simulate accurately the head and flow distribution near a singularity with a finite difference model. Genereux and Bandopadhyay (2001) applied MODFLOW to model the variation of the seepage rate along a lake bed (the seepage rate is defined as the component of the specific discharge vector normal to the lake bed). They observed an elevated seepage rate at the intersection of the straight sloped bank and horizontal bottom of the lake. They stated: `an elevated seepage was observed at the break in bed slope... whenever the surrounding porous medium had a high anisotropy', but drew erroneous conclusions concerning the presence of the singularity: `neither a break in slope nor a high anisotropy alone is sufficient to cause elevated offshore seepage, but together they produce the effect'. An infinite seepage rate is always present at a sharp decrease in slope in a mathematical model of groundwater flow; this is independent of the slope of the side or the anisotropy ratio (e.g. Harr, 1962). However, it may be shown that a steep side or a high anisotropy ratio results in a singular behavior that has an effect over a larger distance; the elevated seepage rate may then be detected with a numerical model with relatively large cell sizes.

The presence of singularities in the mathematical model, the singular behavior, and the effect of anisotropy on the singular behavior will be discussed in this comment by the application of two standard techniques: the hodograph method and a complex variable solution. Flow will be approximated as two-dimensional in the vertical plane. This is not a restriction on the conclusions, because, as Genereux and Bandopadhyay (2001) observed, the singular behavior in two and three dimensions is similar.